When color images are printed on black-and-white printing devices the color information contained in the original image has to be converted or otherwise mapped to black-and-white. This has to be achieved in a manner wherein sufficient color information comprising the color image is retained in the derivative black-and-white image such that the image itself is not lost in the recomposition. Since regions of different color having a similar lightness look about the same, subtle color differences in the original color image can be difficult to distinguish in the resultant black-and-white image. In some instances, this inability to distinguish color differences can compromise the content of the original picture and thereby compromise one's understanding of the resulting graphic or chart.
Colors are generally mapped to textures in order to impose some degree of differentiability other than the density of toner (luminance). Different colors should produce different textures which should be more readily discernible. Methods approach this problem by mapping colors to one or more texture patterns. Alternatively, only primary colors are mapped to texture patterns so that the combinations of primary colors end up being mapped to combinations of texture patterns.
As wavelet theory is important to an understanding of the subject matter of the present invention, the following additional background is provided.
It is well known from Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is also referred to as a Fourier expansion. A disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution meaning that, although all the frequencies present in a signal might be determinable, one does not know when they are present. To overcome this problem, several solutions have been developed which are more or less able to represent a signal in the time and frequency domain at the same time.
The idea behind time-frequency joint representations is to cut the signal of interest into several parts and then analyze the parts separately. It is clear that analyzing a signal this way will give more information about the when and where of different frequency components, but it often leads to a fundamental problem as well: How to cut the signal? Herein lies the problem. Suppose that we want to know exactly all the frequency components present at a certain moment in time. This short time window is cut using a Dirac pulse (f(t)=1 at t=0 and f(t)=0 for all other t), then transform it to the frequency domain.
One problem is that cutting the signal corresponds to a convolution between the signal and the cutting window. Since convolution in the time domain is identical to multiplication in the frequency domain and since the Fourier transform of a Dirac pulse contains all possible frequencies then the frequency components of the signal begin to smear over the frequency axis. This is the opposite of the standard Fourier result as we now have time resolution but no frequency resolution whatsoever. The underlying principle of this problem is due to Heisenberg's uncertainty principle which states, in part, that it is impossible to know the exact frequency and the exact time of occurrence of this frequency in a signal. As such, a signal can not be represented as a point in the time-frequency space.
The wavelet transform or wavelet analysis is one solution to overcome the shortcomings of a Fourier transform. In wavelet analysis, the use of a fully scalable modulated window helps resolve the signal-cutting problem because, as the window is shifted along the signal, the spectrum is calculated for every position. As this process is iterated with a slightly shorter (or longer) window for every cycle, a collection of time-frequency representations of the signal, all with different resolutions, a multi-resolution analysis results.
In the case of wavelets, one does not speak of time-frequency representations but rather time-scale representations, wherein scale is the opposite of frequency as used for Fourier transforms. The large scale is considered the big picture, while the small scales show the details. In a way, going from large scale to small scale is like zooming in on the details.